Question

given that ∠2 is 135°, what other angle is also 135°? a. ∠7 b. ∠3 c. ∠1 d. ∠6

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. $\angle2$ and $\angle4$ are vertical angles, $\angle2$ and $\angle3$ are adjacent angles (linear - pair, sum to 180°), $\angle2$ and $\angle6$ are corresponding angles if the lines are parallel. $\angle2$ and $\angle7$ are alternate exterior angles if the lines are parallel.

Step2: Identify vertical angle of $\angle2$

The vertical angle of $\angle2$ is $\angle4$. Among the given options, we know that vertical angles are equal. $\angle2$ and $\angle4$ are vertical angles. Also, $\angle2$ and $\angle6$ are corresponding angles. If we assume the lines are parallel, corresponding angles are equal. Since $\angle2 = 135^{\circ}$, $\angle6$ is also $135^{\circ}$.

Answer:

D. $\angle6$